Legal Question in Technology Law in California

Not in California, unless you are an undercover police officer or informant.

The answer is no, unless you're speaking about an in-person conversation (rather than telephone) which occurs in a public place.

Just to quibble with the other attorneys, let me point out that there is some (not great) authority for recording a telephone conversation where there are beep sounds every fifteen seconds...

The issue is whether a participant in the phone conversation has a "reasonable expectation of privacy." If there are factors that take away a person's expectation that no one else is tuned in, either on an extension or via a recording device, it is probably legal to eavesdrop or record; an example is the message that "This call may be recorded or monitored for training purposes," etc. Usually in a phone conversation that seems like an "ordinary" two-person conversation, there is an expectation of privacy. That goes away when there are factors suggesting recording or eavesdropping, such as the periodic beep, the warning announcement, or possibly other factors.